It is a requirement to have a 30 minute emergency power source (at least for night/IFR), and a battery is needed for that.
There is no point having an extra generator on an engine because if that engine fails (or runs out of fuel) you lose your source of power. For reasons of control and performance you do not want to be driving a windmilling prop only to keep electricity running. If you had two or more engines to begin with, you will still have power being generated from your remaining engine(s) generators. If you lost your only engine you will be landing within 30 minutes anyway. If you lose your normal electrics on a multi engine, you will be back to your emergency power.
If you have long distances between fields, larger capacity batteries are not much heavier and can give more than the min 30 minutes.